I was wondering how secure cloud Galaxy is if I'm using the default space provided by Galaxy. I've tried using a local instance of galaxy, but it takes DAYS for my computer to map the RNA-Seq reads to a reference genome (tophat). Unfortunately, the data I'm working with are confidential and so I don't want to risk them leaking out. So is galaxy a secure Saas?

this heavily depends on what is the policy you are bound to with the data you are analysing.

Data that are 'confidential' I would not transfer over public networks unencrypted or store on location without my control. In your case I would look into setting up a disposable Galaxy on cloud infrastructure (such as AWS) using Galaxy CloudMan (https://wiki.galaxyproject.org/BigPicture/Choices) and after the analysis finishes and you retrieve the results you can delete that whole instance.

That said I do not know what is the required security and policy of your data so you should discuss this with someone that knows that.